Given: Radius r = 21 mm, ∠AOB = 120°
Perimeter of the minor segment = Length of arc AB + Length of chord AB
Step 1: Length of arc AB
$$l = \frac{\theta}{360} \times 2\pi r = \frac{120}{360} \times 2 \times \frac{22}{7} \times 21 = \frac{1}{3} \times 132 = 44 \text{ mm}$$
Step 2: Length of chord AB
Draw OM ⊥ AB. Then ∠AOM = 60°, OA = 21 mm.
$$AM = OA \times \sin 60° = 21 \times \frac{\sqrt{3}}{2} = \frac{21\sqrt{3}}{2}$$
$$AB = 2 \times AM = 21\sqrt{3} = 21 \times 1.73 = 36.33 \text{ mm}$$
Step 3: Perimeter of shaded (minor segment) region
$$= 44 + 36.33 = \textbf{80.33 mm}$$
Source: Chapter 11, Section 11.1 – Areas of Sector and Segment of a Circle
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